No description available.

In this note, we study the inverse of the Abel transform for the symmetric space ${\bf SU}^{\star}(2n)/{\bf Sp}(n)$. We start by giving a recursive formula for the dual of the Abel transform on the root system $A_{n-1}$. This formula allows us to consider a transmutation property on the generalized Abel transform associated to $A_{n-1}$. / This paper has not been published. However, it has been cited in peer reviewed venues.

Humphreys (1990) defines a simple root system for a finite reflection group which is an important concept fundamental to the understanding of reflection groups as well as Coxeter complexes and Coxeter groups. The proof that Humphreys uses to establish the existence and uniqueness of these systems follows an indirect method that left portions of the proof as exercises to the reader. I present a more complete and direct proof using different organization and methods.

No description available.

In this thesis, we construct Chevalley groups over arbitrary fields. The construction is based on the properties of semi-simple complex Lie algebras, the existence of Chevalley bases and notion of universal enveloping algebras. Using integral lattices in universal enveloping algebras and integral properties of Chevalley bases, we present a method which produces, for any complex simple Lie group, an analogous group over an arbitrary field.

Le mil est une céréale d’importance majeure pour la sécurité alimentaire dans les régions arides d’Afrique et d’Inde. Pourtant, elle a fait l’objet de relativement peu d’efforts d’amélioration variétale par rapport à d’autres céréales. En particulier, l’amélioration de son système racinaire pourrait permettre une amélioration de la tolérance de cette plantes aux contraintes physiques qu’elle subit (sécheresse et faible disponibilité en nutriments) et ainsi un accroissement substantiel de la production. L’objectif de ce travail est de caractériser ce système racinaire, en vue de produire des connaissances nécessaires à l’amélioration variétale, axée principalement sur la tolérance à la sécheresse en début de cycle.Dans un premier temps, nous avons décrit précisément la morphologie du système racinaire dans les premiers stades de développement, la dynamique de mise en place des différents axes racinaires ainsi que l’anatomie des différents types de racines. Ce travail a mis en évidence l’existence de trois types anatomiques distincts pour les racines latérales. Nous avons également mis en évidence l’existence de variabilité dans la dynamique de mise en place précoce du système racinaire au sein d’un panel de diversité issu de variétés cultivées, ce qui ouvre la possibilité d’utiliser cette variabilité existante pour l’amélioration du système racinaire. Notre étude a aussi révélé une grande variabilité des profils de croissances au sein des racines latérales.Pour analyser plus avant cette diversité, la croissance d’un grand nombre de racines latérales a été mesurée quotidiennement et un modèle statistique a permis de classer ces racines latérales en trois grandes tendances, selon leurs profils de croissance. Ces trois catégories distinguent des racines avec des forts taux de croissance, et dont la croissance se poursuit après la fin du suivi, des racines avec des taux de croissance intermédiaires et des racines au taux de croissance faible, qui cessent rapidement de pousser. Ces différents types de racines sont répartis aléatoirement le long de la racine primaire et il ne semble pas y avoir d’influence des types racinaires sur les intervalles entre racines latérales successives. Les trois types cinétiques correspondent, imparfaitement cependant, aux trois types anatomiques mis en évidence dans le premier chapitre. Un travail similaire a été effectué sur le maïs, ce qui a permis de comparer ces deux céréales phylogénétiquement proches.Enfin, nous avons recherché de marqueurs génétiques associés à la croissance de la racine primaire, un trait racinaire supposément impliqué dans la tolérance à la sécheresse précoce. Ce travail a nécessité le phénotypage du trait racinaire en question sur panel de lignées de mil fixées, ce qui a confirmé la présence d’une grande variabilité existante pour ce trait. Ces lignées ont ensuite été génotypées par séquençage. Les analyses d’association génotype/phénotype sont en cours.Ce travail de thèse a permis de caractériser plus précisément le système racinaire du mil, relativement mal connu jusqu’à ce jour. Il a fourni des données utiles pour la paramétrisation et le test de modèles fonctionnels de croissance et de transport d’eau. La caractérisation cinétique précise des types de racines latérales est une approche originale et pourra être utilisée chez d’autres céréales. Enfin, les données acquises par génétique d’association devraient pouvoir servir à une meilleure compréhension de la mise en place de ce système racinaire et ouvrent la voie à l’amélioration assistée par marqueurs génétiques pour des traits racinaires chez le mil. / Pearl millet plays an important role for food security in arid regions of Africa and India. Nevertheless, it lags far behind other cereals in terms of genetic improvement. Improving its root system could improve pearl millet tolerance to abiotic constraints (drought and low nutrient availability) and lead to a significant increase in production. The objective of this work is to characterize pearl system root system development in order to produce knowledge for breeding, mainly targeted on tolerance to drought stress occurring at the early growth stages.First, we described the dynamics of early pearl millet root system development and the anatomy of the different root types. This work revealed the existence of three anatomically distinct types for lateral roots. We also showed the existence of variability in primary root growth and lateral root density in a diversity panel derived from cultivated varieties, which opens the possibility to use this existing variability in root system breeding. Our study also revealed a large variability among the growth profiles of lateral roots.To further analyze this diversity, the growth rates of a large number of lateral roots were measured daily and a statistical model developed to classify these lateral roots into three main trends, according to their growth profiles. These three categories distinguish roots with high growth rate that keep on growing after the end of the experiment, roots with intermediate growth rates and roots with low growth rates that quickly stop growing. These different lateral root types are randomly distributed along the primary root and there seem to be no influence of root types on the intervals between successive lateral roots. The three growth types correspond, though imperfectly, to the three anatomical types evidenced in the first chapter. A similar work has been performed on maize, which was used to compare these two phylogenetically close cereals.Finally, we searched for genetic markers associated to primary root growth, a root trait potentially involved in early drought stress tolerance. A large panel of genetically fixed pearl millet inbred lines was phenotyped, confirming the presence of a large variability existing for this trait. These lines were then genotyped by sequencing. Analyses of association between phenotype and genotype are underway.This work provides a precise description of pearl millet root system that was little studied to date. Our data were used for parameterization and testing of functional structural plant models simulating root growth and water transport. The statistical tool developed for the characterization of the different lateral root growth types is an original approach that can be used on other cereals. Finally, results from our association study will reveal new information on the genetic control of root growth and open the way to marker assisted selection for root traits in pearl millet.

博士(理学) / Doctor of Philosophy in Science / 同志社大学 / Doshisha University

Root systems are a fundamental concept in the theory of Lie algebra. In this thesis, we will use two different kind of graphs to represent the group generated by reflections acting on the elements of the root system. The root systems we are interested in are those of type A2, B2 and G2. After drawing the graphs, we will study the algebraic groups corresponding to those root systems. We will use three different techniques to give a geometric description of the homogeneous spaces G/P where G is the algebraic group corresponding to the root system and P is one of its parabolic subgroup. Finally, we will make a link between the graphs and the multiplication of basis elements in the Chow group CH(G/P).

Plus de la moitié des pertes de bois dans les forêts européennes sont dues aux tempêtes. Une connaissance des mécanismes impliqués dans la stabilité mécanique des arbres est alors capitale. L’ancrage de l’arbre dans le sol constitue l’une des composantes principales du maintien mécanique de l’arbre. Il est principalement déterminé par l’architecture du système racinaire et son interaction mécanique avec le sol. Au cours de son développement, l’arbre modifie ses dimensions et se complexifie. Plus particulièrement, le système racinaire semble s’acclimater (ex : croissance en diamètre plus importante) aux déformations engendrées par le vent. L’ensemble de ces modifications conduit à une évolution des mécanismes à l’origine de l’ancrage au cours du développement de l’arbre. L’étude expérimentale de cette fonction est compliquée car les racines sont difficilement mesurables en continu dans le sol. Nous avons alors mis au point une approche numérique pour décrire la croissance du système racinaire et la distribution des déformations dues au vent. Une grande base de données structurée en chronoséquence de systèmes racinaires numérisés (Pinus pinaster) a été mobilisée. Comme l’étude de la structure et des fonctions des racines est plus efficiente quand la différentiation entre racines est prise en compte, nous avons d’abord formalisé les types racinaires du système racinaire du pin maritime à partir d’une technique de classification (« k-means clustering ») réalisée avec quatre variables. La classification des racines latérales du pin maritime nous a permis d’identifier 5 types racinaires au cours du développement du pin maritime. Ce regroupement explique 70% de la variabilité de notre base de données. Chaque système racinaire est caractérisé par trois grosses racines horizontales émises par la souche. Les racines montrent une forte différentiation pour leur tropisme, avec une direction de croissance soit horizontale soit verticale. La structure de la partie centrale du système racinaire est pratiquement complète dès l'âge de 4 ans. Sur la base des types racinaires identifiés, nous avons calibré un modèle architectural (RootTyp ; Pagès et al. 2004) pour le pin maritime. Treize paramètres pour chaque type racinaire ont été estimés par l’intermédiaire de la base de données, d’informations issues de la littérature et d’une procédure d'optimisation. Une modélisation réaliste du système racinaire jusqu'à 50 ans n’a pu être obtenue qu'en implémentant au modèle RootTyp de nouveaux processus biologiques : la diminution de la ramification avec la croissance de la racine et la diminution de la vigueur des racines avec l'ordre de ramification. Malgré ces améliorations, les systèmes racinaires de la base de données présentent des diamètres plus importants à proximité de la souche par rapport aux systèmes racinaires simulés. Ce biais systématique est principalement attribué à l’acclimatation des racines au vent dominant. Les altérations de croissance dues aux contraintes pédologiques ont également été implémentées grâce à l’amélioration du module de sol du modèle architectural.Enfin, pour comprendre les mécanismes à l’origine de l’acclimatation des racines nous avons combiné plusieurs modèles pour prédire la distribution spatiale des déformations dans des maquettes simplifiées de systèmes racinaires à 4, 6 et 13 ans, pour trois régimes de vent spécifiques à la région étudiée. D’après les simulations, les déformations des racines sous l'effet du vent diminuent avec l’âge, en raison de l’augmentation de la rigidité des racines. Cela suggère une plus forte réponse thigmomorphogénétique aux stades jeunes. Les modifications structurelles et anatomiques du système racinaire par acclimatation au vent s’expliquent principalement par les distributions des déformations et des contraintes dans les racines. / Storms cause more than 50% of the timber loss in European forests. However, forest tree anchorage mechanisms throughout their lifespan are not fully understood, especially the strong acclimation of root systems to common winds. This lack of knowledge is mainly due to technical difficulties: neither the root structure nor the mechanical contribution of the roots could be characterized continually. Thus we set up a numerical approach to model the development of the root system and to describe the strains resulting from common winds. This generic approach has been developed using Pinus pinaster grown in sandy soils as model species.Seven datasets of excavated root systems from 0 to 50 years were employed. The assessment of root structure and functions is more powerful if the differentiation of root system in several root types is considered. We first proposed an automatic classification of roots with the k-means clustering algorithm. Four root traits were chosen as classifiers, including three geometric architectural traits, which can be precisely assessed whatever the tree/root age. Clustering yielded similar five groups of laterals roots at all ages, explaining 70% of the variability. The three largest lateral roots per tree were all horizontal roots branching from stump and the other lateral roots show a large differentiation for tropism: nearly all the roots were horizontal or vertical roots. The framework of the central part of the root system can be almost completed in 4-year-old trees (3.5 cm collar diameter). We then calibrated the existing RootTyp (Pagès et al. 2004) architectural model for P. pinaster for each of the root types defined by the cluster analysis. We used the database combined with a literature review and an optimization method to get accurate values for 13 parameters by root types. We devoted effort to validate our model calibration. In order to model architecture of the root system, damping properties had to be implemented to yield realistic outputs up to the mature stage. Branching varied as a function of distance from the root base, and growth capacity decreased with branching order. Nevertheless, the root diameters of simulated root systems were generally underestimated. This was certainly due to root growth plasticity to the prevailing wind, an acclimation facet not taken into account at this calibration step. Growth alterations due to a cemented horizon were reproduced using the new calibrated soil module. Then, the wind acclimation of roots was numerically investigated by examining the root mechanical stimuli due to wind. A chain of biomechanical models was used to predict the spatial distribution of stress and strain in simplified root systems at 4, 6 and 13-year-old as a result of three levels of usual winds. According to simulations, the strain amplitude decreased with tree growth due to the increasing root system stiffness. This suggests larger thigmomorphogenetic responses at young stages. The modifications of the structural and wood root properties related to wind acclimation were largely explained by the stress and strain distribution in the root system.

Estudos de adubação nitrogenada em cana-de-açúcar normalmente se restringem em avaliar os efeitos no crescimento da parte-aérea. Há evidências de que a fertilização nitrogenada favorece o crescimento de raízes, a absorção de nutrientes e a produtividade da cultura. Objetivou-se com o trabalho avaliar o desenvolvimento de raízes e produtividade da cana-de-açúcar (SP81 3250) nos ciclos de cana-planta e 1ª soca. Foram conduzidos três experimentos, um em LATOSSOLO VERMELHO AMARELO eutrófico (LVAe) e outro em LATOSSOLO VERMELHO distrófico típico (LVd) (ambos de textura média) e um em LATOSSOLO VERMELHO eutrófico (LVe) argiloso. Na cana-planta os tratamentos constaram de doses de nitrogênio (N) de 40, 80 e 120 kg ha-1 e uma testemunha (sem N mineral), em blocos ao acaso, com quatro repetições. Na cana-soca cada parcela da cana-planta foi dividida em quatro subparcelas, às quais foram aplicadas doses de 50, 100 e 150 kg ha-1 N e uma testemunha. No 1º corte o sistema radicular foi avaliado em todos os tratamentos nos três solos. No 2º corte, o sistema radicular foi avaliado somente nas subparcelas dos tratamentos de plantio testemunha e 120 kg ha-1 N, no LVAe e LVd. Para o experimento no solo LVe, somente nas subparcelas testemunha e 150 kg ha-1 N das parcelas principais testemunha e 120 kg ha-1 N foi avaliado o sistema radicular da cana soca. A amostragem de raízes com sonda resultou em massa de raízes que não diferiu da avaliação em monólito, indicando que esse método pode ser usado para avaliações de raízes de cana-de-açúcar. A fertilização nitrogenada de plantio promoveu maior concentração de raízes até 0,2 m no LVd. No ciclo da cana-planta, no LVAe e no LVd houve crescimento pronunciado de raízes de outubro de 2005 a fevereiro de 2006, com redução da massa de fevereiro até a colheita, porém sem afetar o desenvolvimento da parte aérea. Em fevereiro, 20% do N acumulado na planta toda foi encontrado nas raízes, diminuindo para 5% na colheita como decorrência da redução da massa de raízes. As doses de N no plantio favoreceram o crescimento de raízes e a produtividade de colmos no LVAe e no LVe, e o acúmulo de sacarose no LVd. As doses de N na soqueira favoreceram a produtividade de colmos e açúcar nos três solos. No 1º corte, foi obtida maior produtividade de colmos (152 t ha-1) e menor massa de raízes (1,35 t ha-1) no LVe em relação ao LVAe e LVd (139 e 145 t ha-1 de colmos e 2,5 e 2,4 t ha-1 de raízes, respectivamente). Em relação ao 1º corte, a produtividade do 2º corte se manteve estável no LVd (120 t ha-1) e diminuiu drasticamente no LVe (80 t ha-1). Esse fato foi devido à pequena massa de raízes no LVe no 1º corte, tendo em vista que nas duas áreas ocorreu acentuado déficit hídrico em alguns meses antes e após o 1º corte. A adubação nitrogenada de soqueira favoreceu o crescimento de raízes somente no LVe, porém a massa de raízes diminuiu do 1º para o 2º corte, enquanto que no LVAe e no LVd a massa permaneceu constante. / Studies of nitrogen fertilization in sugarcane are usually restricted to evaluations of the effects on growth and productivity of the shoots. There are evidences that nitrogen fertilization favors the growth of roots, the absorption of nutrients and sugarcane productivity. This work was designed to evaluate root development and sugarcane productivity (SP81 3250) in the crop cycles of the cane-plant and of the first ratoon. Three experiments were conducted in a randomized blocks design, with four replications, in three different soils, a Typic Eutrustox (TE) and an Arenic Kandiustults (AK) (both of medium texture), and a clayey Rhodic Eutrustox (RE). Treatments for the cane-plant were nitrogen (N) rates of 0, 40, 80 and 120 kg ha-1 N. In the first ratoon crop each plot of cane-plant was split in four subplots to which rates of 0, 50, 100 and 150 kg ha-1 of N was applied. In the first harvest, the root system was evaluated in all of the treatments applied on the three soils (TE, AK and RE), whereas in the second harvest the root system was evaluated only for the subplots of the planting treatments control and 120 kg ha-1 N in TE and AK. For the experiment in the RE soil, only control and 150 kg ha-1 N subplots of the control and 120 kg ha-1 N main plots had the ratoon root system evaluated. The sampling of roots with probe resulted in a mass of roots that did not differ from the monolith evaluation, indicating that this method can be used for the evaluation of sugarcane roots. Nitrogen fertilization at planting resulted in a higher concentration of roots in the top 0.2 m in AK. There was a pronounced growth of roots in TE and in AK from October, 2005 to February, 2006, and a reduction of the mass from February until harvest; however development of the above ground part of the plant was not affected. Until February, about 20% of accumulated N in the whole plant was found in the roots, decreasing to 5% at harvest, as a consequence of root mass reduction. The N rates applied to the cane-plant favored the roots growth and crop productivity in TE and RE, and the sucrose accumulation in AK. The rates of fertilizer-N in the ratoon favored the productivity of stalks and sugar yield in the three soils. In the first harvest, it was obtained a larger productivity of stalks (152 t ha-1) and a smaller mass of roots (1.35 t ha-1) in RE in relation to TE and AK (139 and 145 t ha-1 of stalks and 2.5 and 2.4 t ha-1 of roots, respectively). The productivity of the second harvest was similar to that of the first harvest in AK (120 t ha-1), but it decreased drastically in RE (80 t ha-1), as a consequence of the small mass of roots in RE in the first harvest, attributed to a high water deficit in the months prior to and after harvest. Nitrogen fertilization applied after the first harvest influenced root growth only in the RE soil; however the mass of roots decreased from the first to the second harvest while in the TE and AK soils the root mass remained constant.